Geometry: Right Triangles, Scale and Views
Primary trigonometric ratios in one and two right triangles, angles of elevation and depression, scale drawings and 3-D views.
11 questions, free, marked as you go with a worked explanation on every one.
What this covers
- math20 3 right triangle trig
- trig ratios
The questions
- A loading ramp rises 0.9 m over a horizontal run of 10.8 m. What angle does the ramp make with the ground, in degrees, rounded to one decimal place?
- A surveyor stands 25 m from the base of a grain elevator. The angle of elevation from her eyes to the top is 38°, and her eyes are 1.7 m above the ground. How tall is the elevator, in metres, rounded to one decimal place?
- A guy wire 12 m long runs from the top of a pole to the ground, making an angle of 55° with the ground. How high up the pole is the wire attached, in metres, rounded to one decimal place?
- A blueprint is drawn at a scale of 1 : 40. On the blueprint a wall measures 32 cm. How long is the actual wall, in metres?
- A machinist must build a scale model of a 15 m bridge at a scale of 1 : 250. How long should the model be, in centimetres?
- An apprentice is given the top, front and side views of a machine part. What is the main advantage of these three views over a single perspective drawing?
- Flat-pack furniture is usually supplied with an exploded-view diagram. What does an exploded view show that an assembled drawing does not?
- A surveyor measures a tall antenna in two steps. From point A the angle of elevation to the top is 30°, and from point B, 40 m closer along the same straight line, the angle of elevation is 50°. How tall is the antenna, in metres, rounded to one decimal place?
- A right triangle has an opposite side of 9 cm and an adjacent side of 12 cm to a given angle. Find that angle, to the nearest tenth of a degree.
- In a right triangle, an angle measures 25 degrees and the hypotenuse is 15 cm. Find the length of the side opposite that angle, to the nearest tenth of a centimetre.
- From the top of a 6 m tower, the angle of depression to a parked car is 15 degrees. Find the horizontal distance from the base of the tower to the car, to the nearest tenth of a metre.